A beam codebook of 5G millimeter wave (mmWave) for data communication consists of multiple high-peak-gain beams to compensate the high pathloss at the mmWave bands. These beams also have to point to different angular directions, such that by performing beam searching over the codebook, a good mmWave signal coverage over the full sphere around the terminal (spherical coverage) can be achieved. A model-based beam codebook design that assumes ideal omni-directional antenna pattern, and neglects the impact of terminal housing around the antenna, does not work well because the radiation pattern of a practical mmWave antenna combined with the impact of terminal housing is highly irregular. In this paper, we propose a novel and efficient data-driven method to generate a beam codebook to boost the spherical coverage of mmWave terminals. The method takes as inputs the measured or simulated electric field response data of each antenna and provides the codebook according to the requirements on the codebook size, spherical coverage, etc. The method can be applied in a straightforward manner to different antenna type, antenna array configuration, placement and terminal housing design. Our simulation results show that the proposed method generates a codebook better than the benchmark and 802.15.3c codebooks in terms of the spherical coverage.